∫xdx2x2+3x2−1 is equal to - Infinity Learn by Sri Chaitanya

A
$\tan^{- 1} (\sqrt{\frac{2}{5}} \sqrt{x^{2} - 1}) + C$
B
$10 \tan^{- 1} (\sqrt{\frac{2}{5}} \cdot \sqrt{x^{2} - 1}) + C$
C
$\frac{1}{\sqrt{10}} \tan^{- 1} (\sqrt{\frac{2}{5}} \cdot \sqrt{x^{2} - 1}) + C$
D
None of these

Solution:

$\begin{array}{l} Put x^{2} - 1 = t^{2} \Rightarrow xdx = tdt \\ \begin{aligned} so, I & = \int \frac{tdt}{(2 t^{2} + 5) t} \\ = \int \frac{dt}{2 t^{2} + 5} = \frac{1}{2} \int \frac{dt}{t^{2} + \frac{5}{2}} = \frac{1}{\sqrt{10}} \tan^{- 1} (\sqrt{\frac{2}{5}} \sqrt{x^{2} - 1}) + C \end{aligned} \end{array}$

$\int \frac{xdx}{(2 x^{2} + 3) \sqrt{x^{2} - 1}}$ is equal to

Solution:

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